Investigations Blog

A Grade 3 Q&A: Why start with multiplication and division?

Question: Why does 3rd grade start with a multiplication/division unit and not addition/subtraction? Answer: We often hear from people who wonder why Grade 3 starts with a multiplication and division unit—just like it did in the 1st edition!—rather than an addition and subtraction unit. As we decided on the sequence of the units in any grade, we considered many different things. The most important was the development of mathematical content within and across grades. In Investigations 3,...

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A Kindergarten Q&A: Numbers Represent Quantities

As we said in the original post, our ideas for our blog are wide-ranging. We are excited to have a space that offers us the opportunity to answer common questions from the field. This Q&A is the first of that type of blog post. Have questions you’d like to see answered? Email us. Question: How do Kindergarteners learn to write the numbers, and use them to represent quantities? Answer: We are frequently asked about how Investigations supports young students in the development of numeral...

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Using Tools in Art and Math

Recently, I was chatting with a 7-year-old I know pretty well. I asked her about school, and she quickly started telling me about her current math work, complete with eye rolls and boredom. I decided to change the subject a little. “I know you like to tell me about math because I love math, but what’s your favorite subject?” I asked. She thought for a moment and then said, “Art.” Art was never my favorite subject. I’m not even sure I’ve passed stick figure drawing yet. “Why?” I asked. She...

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Puzzling Through Making Fraction Sets

Last year I volunteered in a third grade class. The school mainly uses Investigations 3. During a visit last spring, the class was working on the second session of the fractions unit. I was excited to find out about the students’ beginning understandings of fractions. I sat with a group of four students who were working on making fraction sets. Their task was to fold each of 5 sheets of paper into two, three, four, five, and six equal parts and then to label each piece. The students made 4...

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“What Was Thomas Thinking?”

I often think about a lesson, captured on video some years ago. Liz, a fifth-grade teacher, gave her students two-digit multiplication problems—12 × 29 and 36 × 17— and asked them to come up with strategies other than the conventional algorithm to perform the calculation. For 12 × 29, Jemea thought about twelve 30s and then subtracted 1 for each of 12 groups. 360 – 12 = 348. For 36 × 17, Duane thought of 36 bowls, each holding 17 cotton balls. Ten bowls hold 170 cotton balls, and there are...

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¡Gracias, Myriam, y Hasta Luego!

Our colleague, Myriam Steinback, is heading off on a new adventure. Her departure, after 21 years directing Investigations Workshops, gives us the opportunity to reflect on her work and contributions. Investigations professional development provides opportunities for teachers to engage in mathematics, in the ways that embody the Investigations philosophy. It focuses on how children learn, how mathematical ideas develop within and across the grades, and on examining student thinking and student...

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Incomplete, inarticulate, ill-formed, incorrect: Brilliant!

Over the last decade, much of my work has been focused on mathematical argument in the elementary classroom. Observing in our collaborating classrooms, I was struck again and again by how teachers supported students to build on each other’s incomplete ideas. Constructing a mathematical argument is difficult and challenging for elementary students and, therefore, necessarily collaborative. When students are learning what it means to make an argument, not just about the solution to a single...

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From “Uh Oh!” to “Aha!”

Over 20 years ago, just out of college, I applied for a job at TERC after seeing an ad in a newspaper. A project called Investigations in Number, Data, and Space was looking for a classroom observer. I had spent most of my college years volunteering in an elementary classroom once a week, so I sent a writing sample – from a course I’d taken with Ted Sizer – and got an interview. The last step? Meet Susan Jo Russell, the Principal Investigator of the project. We chatted and...

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Curriculum Matters

Picture it! J.M. Ullom ES, Las Vegas, NV, 5th grade classroom, 1992-1993. (Yes, there are schools in Las Vegas!) It was my 11th year of teaching. I’d taught 7th and 8th grade on two Native American Nations in Arizona, and had been teaching 5th grade in Las Vegas for four years. I’d been fortunate enough to receive high-quality professional development and was part of a math leadership project focused on Grades 3-5. I was slowly changing the way I taught mathematics, relying less and less on...

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It’s Not What’s New; It’s What’s Old

People often ask me, “What’s your favorite part of the new edition of Investigations?” My first inclination is to blurt out “That it’s finished!”, despite the fact that the development stage has been over for almost a year. While many aspects of the revision were engaging and rewarding, I’m sure that someday soon I will not cringe when I hear the word deadline! That said, I think I can honestly say that my favorite part of the 3rd edition is also my favorite part of the 1st and...

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